Bifurcation in kinetic equation for interacting Fermi systems.

Area of Science:

• Quantum kinetic theory
• Statistical mechanics
• Condensed matter physics

Background:

• Dense interacting Fermi systems are crucial in understanding many-body quantum phenomena.
• Existing kinetic equations often struggle to capture complex dynamics like chaos and delayed effects.
• Microscopic delay times are fundamental to deterministic chaotic systems.

Purpose of the Study:

• To introduce and analyze a novel nonlocal quantum kinetic equation for dense Fermi systems.
• To investigate the emergence of oscillations and bifurcations in the system's time evolution.
• To identify conditions leading to chaotic behavior and potential phase transitions.

Main Methods:

• Derivation of a continuous delay differential equation incorporating time derivatives and finite time stepping.
• Explicit calculation and analysis of the microscopic delay time for short-range correlations.
• Examination of the time evolution of the distribution function under varying temperature and density conditions.

Main Results:

• The nonlocal quantum kinetic equation exhibits novel oscillations in the distribution function's time evolution.
• Bifurcations leading to chaotic behavior are observed under specific temperature and density conditions.
• The study explicitly calculates the delay time relevant to the deterministic chaotic system dynamics.

Conclusions:

• The derived equation provides a new framework for studying quantum chaos in dense Fermi systems.
• Oscillations and bifurcations signal a potential onset of phase transitions in these systems.
• Understanding these phenomena is key to advancing the theory of quantum many-body systems.